-
Notifications
You must be signed in to change notification settings - Fork 83
/
occupation.jl
245 lines (218 loc) · 11.7 KB
/
occupation.jl
1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
78
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
119
120
121
122
123
124
125
126
127
128
129
130
131
132
133
134
135
136
137
138
139
140
141
142
143
144
145
146
147
148
149
150
151
152
153
154
155
156
157
158
159
160
161
162
163
164
165
166
167
168
169
170
171
172
173
174
175
176
177
178
179
180
181
182
183
184
185
186
187
188
189
190
191
192
193
194
195
196
197
198
199
200
201
202
203
204
205
206
207
208
209
210
211
212
213
214
215
216
217
218
219
220
221
222
223
224
225
226
227
228
229
230
231
232
233
234
235
236
237
238
239
240
241
242
243
244
245
@testsetup module Occupation
using DFTK
smearing_methods = (
DFTK.Smearing.None(),
DFTK.Smearing.FermiDirac(),
DFTK.Smearing.Gaussian(),
DFTK.Smearing.MarzariVanderbilt(),
DFTK.Smearing.MethfesselPaxton.(1:4)...
)
fermialgs = (
FermiBisection(),
FermiTwoStage(),
)
end
@testitem "Smearing functions" setup=[Occupation] begin
using DFTK
for m in Occupation.smearing_methods
@test DFTK.Smearing.occupation(m, -Inf) == 1
@test DFTK.Smearing.occupation(m, Inf) == 0
x = .04
ε = 1e-8
@test abs((DFTK.Smearing.occupation(m, x+ε) - DFTK.Smearing.occupation(m, x))/ε -
DFTK.Smearing.occupation_derivative(m, x)) < 1e-4
# entropy functions should satisfy s' = x f'
sprime = (DFTK.Smearing.entropy(m, x+ε) - DFTK.Smearing.entropy(m, x))/ε
fprime = (DFTK.Smearing.occupation(m, x+ε) - DFTK.Smearing.occupation(m, x))/ε
@test abs(sprime - x*fprime) < 1e-4
end
end
@testitem "Smearing for insulators" tags=[:dont_test_mpi] setup=[Occupation, TestCases] begin
using DFTK: FermiZeroTemperature
using Logging
silicon = TestCases.silicon
Ecut = 5
n_bands = 10
fft_size = [15, 15, 15]
# Emulate an insulator ... prepare energy levels
n_k = length(silicon.kgrid)
eigenvalues = [zeros(n_bands) for _ = 1:n_k]
n_occ = div(silicon.n_electrons, 2, RoundUp)
for ik = 1:n_k
eigenvalues[ik] = sort(rand(n_bands))
eigenvalues[ik][n_occ+1:end] .+= 2
end
εHOMO = maximum(eigenvalues[ik][n_occ] for ik = 1:n_k)
εLUMO = minimum(eigenvalues[ik][n_occ + 1] for ik = 1:n_k)
# Occupation for zero temperature
occupation0 = let
model = Model(silicon.lattice, silicon.atoms, silicon.positions;
temperature=0.0, terms=[Kinetic()])
basis = PlaneWaveBasis(model; Ecut, silicon.kgrid, fft_size)
occupation, εF = DFTK.compute_occupation(basis, eigenvalues, FermiZeroTemperature())
@test εHOMO < εF < εLUMO
@test DFTK.weighted_ksum(basis, sum.(occupation)) ≈ model.n_electrons
occupation
end
# See that the electron count still works if we add temperature
for temperature in (0, 1e-6, .1, 1.0), smearing in Occupation.smearing_methods,
alg in Occupation.fermialgs
model = Model(silicon.lattice, silicon.atoms, silicon.positions;
temperature, smearing, terms=[Kinetic()])
basis = PlaneWaveBasis(model; Ecut, silicon.kgrid, fft_size)
occs = with_logger(NullLogger()) do
DFTK.compute_occupation(basis, eigenvalues, alg; tol_n_elec=1e-12).occupation
end
@test sum(basis.kweights .* sum.(occs)) ≈ model.n_electrons
end
# See that the occupation is largely uneffected with only a bit of temperature
for temperature in (0, 1e-6, 1e-4), smearing in Occupation.smearing_methods,
alg in Occupation.fermialgs
model = Model(silicon.lattice, silicon.atoms, silicon.positions;
temperature, smearing, terms=[Kinetic()])
basis = PlaneWaveBasis(model; Ecut, silicon.kgrid, fft_size)
(; occupation) = DFTK.compute_occupation(basis, eigenvalues, alg; tol_n_elec=1e-6)
for ik = 1:n_k
@test all(isapprox.(occupation[ik], occupation0[ik]; atol=1e-2))
end
end
end
@testitem "Smearing for a simple metal" #=
=# tags=[:dont_test_mpi] setup=[Occupation, TestCases] begin
using DFTK
using Logging
(; silicon, magnesium) = TestCases.all_testcases
# Note: Mixture of silicon and magnesium is on purpose
model = Model(silicon.lattice, magnesium.atoms, magnesium.positions;
n_electrons=magnesium.n_electrons, temperature=1e-2, terms=[Kinetic()])
basis = PlaneWaveBasis(model; Ecut=5, kgrid=[2, 3, 4], kshift=[1, 0, 1]/2)
# Emulate a metal ...
eigenvalues = [[-0.08063210585291, 0.11227915155236, 0.13057816014162, 0.57672256037074],
[ 0.09509047528102, 0.09538152469111, 0.27197836572013, 0.28750689088845],
[-0.00144586520885, 0.18640677556553, 0.19603060374450, 0.24422060327989],
[ 0.05693643182609, 0.16919740718547, 0.24190245274401, 0.25674283154835],
[-0.06756541677784, 0.03381889875058, 0.23162853469956, 0.50981867707851],
[ 0.10685980948954, 0.10728887405642, 0.20784971952147, 0.20786603845828],
[ 0.01122399002894, 0.11011069317735, 0.24016826005369, 0.30770620467001],
[ 0.06925846412968, 0.16087157153058, 0.19146746736359, 0.27463770659603],
[-0.02937886574534, -0.02937886574483, 0.36206906745747, 0.36206906745749],
[ 0.13314087354890, 0.13314087354890, 0.15834732772541, 0.15834732772541],
[ 0.04869672986772, 0.04869672986772, 0.27749728805752, 0.27749728805768],
[ 0.10585630776222, 0.10585630776223, 0.22191839818805, 0.22191839818822]]
@assert length(basis.kpoints) == length(eigenvalues)
parameters = (
(DFTK.Smearing.FermiDirac(), 0.01, 0.16163115311626172),
(DFTK.Smearing.FermiDirac(), 0.02, 0.1624111568340279),
(DFTK.Smearing.FermiDirac(), 0.03, 0.1630075080960013),
(DFTK.Smearing.MethfesselPaxton(1), 0.01, 0.16120395021955866),
(DFTK.Smearing.MethfesselPaxton(1), 0.02, 0.16153528960704408),
(DFTK.Smearing.MethfesselPaxton(1), 0.03, 0.16131173898225953),
)
for (smearing, temperature, εF_ref) in parameters, alg in Occupation.fermialgs
occupation, εF = with_logger(NullLogger()) do
DFTK.compute_occupation(basis, eigenvalues, alg; smearing, temperature,
tol_n_elec=1e-10)
end
@test DFTK.weighted_ksum(basis, sum.(occupation)) ≈ model.n_electrons
@test εF ≈ εF_ref
end
end
@testitem "Fermi level finding for smearing multiple εF" #=
=# tags=[:dont_test_mpi] setup=[Occupation, TestCases] begin
using DFTK
using Logging
iron_bcc = TestCases.iron_bcc
# This is an iron setup, which caused trouble in the past
#
model = Model(iron_bcc.lattice, iron_bcc.atoms, iron_bcc.positions;
n_electrons=iron_bcc.n_electrons, temperature=1e-2, terms=[Kinetic()],
magnetic_moments=[4])
basis = PlaneWaveBasis(model; Ecut=5, kgrid=(4, 4, 4))
eigenvalues = [
[-0.09317171, 0.05662733, 0.05662733, 0.05662733, 0.1027973, 0.1027973, 1.133822],
[-0.01970275, 0.04049757, 0.06672252, 0.09504781, 0.09571417, 0.1045477, 0.777691],
[-0.008317428, 0.02549644, 0.1018706, 0.1075814, 0.140451, 0.2306614, 0.4425744],
[0.01779316, 0.03559934, 0.06175814, 0.09824229, 0.1133369, 0.2534185, 0.598366],
[0.03831527, 0.03831527, 0.03831527, 0.1085794, 0.1085794, 0.5062097, 0.5062097],
[0.02249843, 0.04778311, 0.07322733, 0.07322733, 0.09343694, 0.1691936, 0.8155277],
[0.01298261, 0.03133082, 0.07131262, 0.0928459, 0.1361777, 0.3808009, 0.4713903],
[-0.006884875, -0.006884875, 0.1317392, 0.1317392, 0.1317392, 0.560895, 0.560895],
[-0.0686855, 0.3042072, 0.3042072, 0.3042072, 0.3824597, 0.3824597, 1.141987],
[0.01739212, 0.2749508, 0.2790246, 0.3584238, 0.3687848, 0.3864797, 0.8680247],
[0.1453898, 0.2491354, 0.2495129, 0.3776472, 0.3951613, 0.4310432, 0.6072722],
[0.1478936, 0.2322534, 0.2519767, 0.3713906, 0.3948955, 0.4582024, 0.707126],
[0.2196432, 0.2196432, 0.2196432, 0.3973532, 0.3973532, 0.632154, 0.632154],
[0.09041911, 0.2750986, 0.312412, 0.312412, 0.3584034, 0.4077667, 0.9012088],
[0.1944933, 0.2061272, 0.3099407, 0.3365089, 0.4243378, 0.4929272, 0.599024],
[0.1830541, 0.1830541, 0.417559, 0.417559, 0.417559, 0.5923824, 0.5923824],
]
@assert length(basis.kpoints) == length(eigenvalues)
parameters = ( # # other εF with +ve DOS
(DFTK.Smearing.Gaussian(), 1e-2, 0.26725860386964656),
(DFTK.Smearing.MarzariVanderbilt(), 1e-2, 0.2624352644962286),
(DFTK.Smearing.MethfesselPaxton(1), 1e-2, 0.2685411900311375),
(DFTK.Smearing.MethfesselPaxton(2), 1e-2, 0.2627127425669326), # 0.2713096607939751
(DFTK.Smearing.MethfesselPaxton(5), 1e-2, 0.2614680485215832), # 0.2724701412295064
(DFTK.Smearing.Gaussian(), 1e-3, 0.27413279592006573),
(DFTK.Smearing.MarzariVanderbilt(), 1e-3, 0.2744172412944558),
(DFTK.Smearing.MethfesselPaxton(1), 1e-3, 0.27445994971377974),
(DFTK.Smearing.MethfesselPaxton(2), 1e-3, 0.2745745124212358),
(DFTK.Smearing.MethfesselPaxton(5), 1e-3, 0.2747069248135472),
(DFTK.Smearing.Gaussian(), 1e-4, 0.27488223611466617),
(DFTK.Smearing.MarzariVanderbilt(), 1e-4, 0.27490853712608),
(DFTK.Smearing.MethfesselPaxton(1), 1e-4, 0.274908008227603),
(DFTK.Smearing.MethfesselPaxton(2), 1e-4, 0.27491607692918685),
(DFTK.Smearing.MethfesselPaxton(5), 1e-4, 0.2749270541035508),
)
for (smearing, temperature, εF_ref) in parameters
fermialg = DFTK.default_fermialg(smearing) # TODO Test others
occupation, εF = with_logger(NullLogger()) do
DFTK.compute_occupation(basis, eigenvalues, fermialg; smearing, temperature)
end
@test DFTK.weighted_ksum(basis, sum.(occupation)) ≈ model.n_electrons
@test εF ≈ εF_ref
end
end
@testitem "Density for smearing with multiple εF" setup=[Occupation, TestCases] begin
using DFTK
testcase = TestCases.iron_bcc
magnetic_moments = [4.0]
model = model_PBE(testcase.lattice, testcase.atoms, testcase.positions;
temperature=1e-2, smearing=Smearing.Gaussian(), magnetic_moments)
basis = PlaneWaveBasis(model; Ecut=10, kgrid=[4, 4, 4])
scfres = self_consistent_field(basis; ρ=guess_density(basis, magnetic_moments), tol=1e-4)
for temperature in (1e-4, 1e-3, 1e-2), smearing in Occupation.smearing_methods,
alg in Occupation.fermialgs
smearing isa Smearing.None && continue
occupation, εF = DFTK.compute_occupation(scfres.basis, scfres.eigenvalues, alg;
smearing, temperature)
ρ = DFTK.compute_density(scfres.basis, scfres.ψ, scfres.occupation;
scfres.occupation_threshold)
atol = scfres.occupation_threshold
@test DFTK.weighted_ksum(basis, sum.(occupation)) ≈ model.n_electrons atol=atol
@test sum(ρ) * scfres.basis.dvol ≈ model.n_electrons atol=atol
end
end
@testitem "Fixed Fermi level" tags=[:dont_test_mpi] setup=[TestCases] begin
using DFTK
testcase = TestCases.magnesium
function run_scf(; kwargs...)
atoms = fill(ElementGaussian(1.0, 0.5), length(testcase.positions))
model = Model(testcase.lattice, atoms, testcase.positions;
temperature=0.01, disable_electrostatics_check=true, kwargs...)
basis = PlaneWaveBasis(model; Ecut=5, kgrid=(2, 2, 2))
self_consistent_field(basis; nbandsalg=FixedBands(; n_bands_converge=8))
end
scfres_ref = run_scf(; testcase.n_electrons)
εF_ref = scfres_ref.εF
n_electrons_ref = scfres_ref.basis.model.n_electrons
@test n_electrons_ref == testcase.n_electrons
δεF = εF_ref / 4
for εF in [εF_ref - δεF, εF_ref + δεF]
scfres = run_scf(; εF)
@test εF ≈ scfres.εF
n_electrons = DFTK.weighted_ksum(scfres.basis, sum.(scfres.occupation))
εF > εF_ref && @test n_electrons > n_electrons_ref
εF < εF_ref && @test n_electrons < n_electrons_ref
end
end